MaST is the Masters level study programme I am on (standing for Mathematics Specialist Teacher). HEI merely stands for Higher Education Day.
Creativity in Maths
The Day begin with a lecture on creativity in maths. It's an interesting idea – creativity – because many teachers have the mental construct that creativity is all about thinking artisticly and creating things of aesthetic value. Derek Haylock went on to talk about about divergence and flexibility – a far different way concept of creativity in maths. One leads to trying to shoe-horn maths into a themed curriculum and doing lots of shape work that becomes artwork, the other leads to open-ended questions, good dialogue and child-centred learning. Here are my tweets:
- About to hear Dr. Derek Haylock at #MaSThei5. http://derek-haylock.blogspot.com
- #MaSThei5 creativity is not normally associated with mathematics (confusion between artistic and creativity)
- #MaSThei5 find 2 numbers with a sum of 9 and a difference of 4? When we have the knowledge, what blocks us accessing it to solve a problem?
- #masthei5 what are the processes that characterise creative thinking? How do we recognise creative product What kind of people are creative?
- #masthei5 what conditions foster creative thinking? (all in maths context)
- #masthei5 Derek Haylock demonstrate that we're all fixed, rigid thinkers by nature. We have to choose to think flexibly.
- #masthei5. Equal pieces problem – will demonstrate on blog how we're all rigid by nature.
- #masthei5 flexible thinking is the first step on a creative process in maths. Avoid rigidity an fixation.
- #masthei5 2 kinds of fixation common in maths that limit creativity: algorithmic and content universe
- #masthei5 ask children to draw a rectangle. What do most of them do?
- #masthei5 creativity in maths includes thinking divergently: fluency (many), flexibility (kinds), originality, appropriateness.
- #Masthei5 appropriateness is easy to define in maths (as opposed to art, writing, etc) so teachers fixate on this one part of divergence
- #masthei5 how to develop divergent thinking in maths: problems with many solutions; problem-posing; redefinition.
- #masthei5 redefinition – come up with lots of responses by redefining the elements, eg: what's the same as 16 and 36?
- #masthei5 redefine by using lots of different ideas to create subsets of a given set of numbers
- #masthei5 conflict between creativity an accuracy – do we value creativity as much as accuracy in maths?
- #masthei5 graph of attainment vs. creativity (as Derek Haylock defines it) show 0 children in the high creativity, low attainment sector
- #masthei5 factors associated with maths creativity include low anxiety, high self-concept, risk-taker, high attainer, being a boy.
- #masthei5 creative maths children are also 'broad categorisors'. They are good at identifying the same about numbers+ideas and make links.
Course Tutor, Mary McAteer gave us some top tips and hints to help us successfully write our first piece of level 7 writing.
- #masthei5 Mary McAteer reminds us to demonstrate an understanding of ethical issues in essay and PLL
- #masthei5 warns us against over use of Excel as a presentational tool for simple data
Ian Sugarman definitely had the graveyard shift on the day. The last session after a big lunch on a 6 day week – on a Saturday when most would be out shopping, or slobbing in front of the TV – can't have been an easy lecture. And when the subject is the dry area of place value, it's always going to be a tricky one. The biggest thing I got out of this lecture is the warning against the indiscriminate use of number lines and the value of teacher column methods for securing place value when ordering decimals.
- Context for place value #masthei5 getting things 10 times out can be at best expensive; at worst lethal…
- #masthei5 misconceptions of place value after the decimal point are rife between ages of 7-11. Half-learned rules and over-generalisations
- #masthei5 when pupils are given opportunities to explain their thinking, they often spot their own flaws.
- #masthei5 to get place value it's helpful to sort and justify before ordering
- #masthei5 talks about left-justifying decimals when I think it's helpful to justify by the decimal point
- #masthei5 to get x10 relationship it's helpful to use pictures or Dienes apparatus to visualise place value
- #masthei5 recommends http://nlvm.usu.edu – university of Utah website for good models and images.
- Great activities advertised at #masthei5 at http://numbergym.co.uk (but not free)
- At #masthei5 Ian Sugarman talks about standard algorithms can be a sledgehammer to crack a nut in questions like 81-78.
- #masthei5 numberlines vs standard algorithms vs necessity of getting place value = conflicting interests
- #masthei5 British children have been referred to as 'pathological splitters', as they partition numbers in both addition and subtraction.
- #masthei5 Ian Sugarman advocates empty number lines, but not as another rote-learned method. Draw from 0 and emphasize progression.
- #masthei5 maths in Holland always starts with a real setting, whereas in UK we start with pure maths.
- #masthei5 can use 'same difference' method as alternative to empty number line for examples such as 83-37 (86-40 is much easier)